The auth0| prefix is not specific to the Management API, it will always be added to a user even if you create them via Dashboard or if a user signs up. This is to identify various types of objects (MFA methods with email| or phone|, roles with rol_, etc.)
To make things more clearly I am describing a scenario we face:
Let’s say we are running backups our selves for all social and database connections, looking at one account of those connections: we backup the user_id with “oauth2|Social-Con|auth0|12345”. Now something happens to the connections and all users are gone. We want to recover that specific user, thus creating a new user with the backed up infos. Now the user_id will be “auth0|oauth2|Social-Con|auth0|12345” and cannot be assigned to that specific in our system still existing user because the id’s will never match, plus if you think this process a couple times through you will endup with user_ids like this: auth0|auth0|auth0|auth0…
Sadly, the self-backup/restore scenario you describe would not be possible for Social connections. And neither would it be possible for non Custom Database connections. It’s not currently possible to create a Social Connection in Auth0 directly via the Management API, so recovery of a Social account would require the user to perform first factor authentication again with the social provider; even then the user_id associated with the account could not be guaranteed as this is based on the (user) identifier that comes from the social provided - which may have changed. It’s also not possible to control the user_id generated for a user account associated with an Auth0 managed Database connection: identifiers for Auth0 Database connections are uniquely generated, so a new identifier would typically be created even if you re-created the user account via use of the Auth0 Management API.